Exact Characterization of Aggregate Flexibility via Generalized Polymatroids

2025-03-30

AI Summary

High computational complexity and poor scalability of Minkowski sum operations hinder flexibility aggregation for distributed energy resource (DER) clusters. Method: This paper pioneers the application of generalized matroid polytopes to characterize structural commonalities across individual DER flexibility sets; based on this insight, it derives a compact and exact aggregated flexibility representation for homogeneous DER populations and designs a vertex-driven, computationally efficient decoupling allocation algorithm. Contribution/Results: The proposed framework achieves theoretical optimality and polynomial-time scalability. In large-scale scenarios, its computational efficiency exceeds that of state-of-the-art methods by over an order of magnitude, significantly enhancing modeling accuracy, computational tractability, and dispatch practicality of aggregated flexibility.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

There is growing interest in utilizing the flexibility in populations of distributed energy resources (DER) to mitigate the intermittency and uncertainty of renewable generation and provide additional grid services. To enable this, aggregators must effectively represent the flexibility in the populations they control to the market or system operator. A key challenge is accurately computing the aggregate flexibility of a population, which can be formally expressed as the Minkowski sum of a collection of polytopes - a problem that is generally computationally intractable. However, the flexibility polytopes of many DERs exhibit structural symmetries that can be exploited for computational efficiency. To this end, we introduce generalized polymatroids - a family of polytope - into the flexibility aggregation literature. We demonstrate that individual flexibility sets belong to this family, enabling efficient computation of their Minkowski sum. For homogeneous populations of DERs we further derive simplifications that yield more succinct representations of aggregate flexibility. Additionally, we develop an efficient optimization framework over these sets and propose a vertex-based disaggregation method, to allocate aggregate flexibility among individual DERs. Finally, we validate the optimality and computational efficiency of our approach through comparisons with existing methods.

Problem

• Characterizing aggregate flexibility of distributed energy resources
• Efficiently computing Minkowski sum of flexibility polytopes
• Allocating aggregate flexibility among individual DERs optimally

Innovation

• Utilizes generalized polymatroids for flexibility aggregation
• Efficiently computes Minkowski sum of flexibility polytopes
• Develops vertex-based disaggregation for DER allocation